There have already been proposed by the applicant of the present application techniques for controlling the air-fuel ratio of an air-fuel mixture to be combusted by an internal combustion engine for converging the output of an exhaust gas sensor, e.g., an O2 sensor (oxygen concentration sensor), disposed downstream of a catalytic converter, to a predetermined target value (constant value) in order to achieve the appropriate purifying capability of the catalytic converter, such as a three-way catalyst or the like, disposed in the exhaust gas passage of the internal combustion engine (e.g., see Japanese laid-open patent publication No. 11-324767 or U.S. Pat. No. 6,188,953, and Japanese laid-open patent publication No. 2000-179385 or U.S. Pat. No. 6,230,486).
According to these techniques, an exhaust system ranging from a position upstream of the catalytic converter to the O2 sensor disposed downstream of the catalytic converter is an object to be controlled which has an input quantity represented by the air-fuel ratio of the exhaust gas that enters the catalytic converter and an output quantity represented by the output of the O2 sensor. A manipulated variable which determines the input quantity of the exhaust system, e.g., a target value for the input quantity of the exhaust system, is sequentially generated by a feedback control process, or specifically an adaptive sliding mode control process, for converging the output of the O2 sensor to the target value, and the air-fuel ratio of the air-fuel mixture to be combusted by the internal combustion engine is controlled depending on the manipulated variable.
Generally, the exhaust system including the catalytic converter has a relatively long dead time. The dead time of a system for generating an actual input quantity of the exhaust system from the manipulated variable, i.e., an air-fuel ratio manipulating system comprising the internal combustion engine, etc., is generally smaller than the dead time of the exhaust system, but may become relatively long depending on the operating state of the internal combustion engine. These dead times tend to present an obstacle to efforts to smoothly controlling the output of the O2 sensor at the target value.
According to the above techniques, data representing an estimated value of the output of the O2 sensor after the dead time of the exhaust system, or after a total dead time which is the sum of the dead time of the exhaust system and the dead time of the air-fuel ratio manipulating system, is sequentially calculated according to a predetermined estimating algorithm that is constructed based on a predetermined model of the exhaust system, etc. In the feedback control process for generating the manipulated variable, the estimated value of the output of the O2 sensor is used to generate the manipulated variable. That is, the manipulated variable is generated to converge the estimated value to the target value.
According to the above techniques, the value of a predetermined parameter of the model of the exhaust system which serves as a basis for the estimating algorithm is sequentially identified using sampled data of the output of an air-fuel ratio sensor disposed upstream of the catalytic converter and the output of the O2 sensor. The estimating algorithm uses the identified value of the parameter of the model of the exhaust system to estimate the output of the O2 sensor.
By performing the above control procedure, the above techniques can compensate for the effect of the dead times of the exhaust system and the air-fuel ratio manipulating system and also for the effect of behavioral changes of the exhaust system, and stably and smoothly perform the control process for converging the output of the O2 sensor to the target value, or stated otherwise, the control process for achieving an appropriate purifying capability of the catalytic converter.
According to the above techniques, basically, the dead times of the exhaust system and the dead time of the air-fuel ratio manipulating system are regarded as of constant values, and preset fixed dead times are used as the values of those dead times. In the process of estimating the output of the O2 sensor, the output of the O2 sensor after the preset dead time of the exhaust system, and the output of the O2 sensor after the total preset fixed dead time which is the sum of the preset dead time of the exhaust system and the preset dead time of the air-fuel ratio manipulating system are sequentially estimated.
The inventors of the present application have found that the actual dead times of the exhaust system and the air-fuel ratio manipulating system vary depending on the state, such as the rotational speed, of the internal combustion engine. Particularly, the range in which the dead time of the exhaust system is variable may become relatively large depending on the operating state of the internal combustion engine. Consequently, depending on the operating state of the internal combustion engine, the estimated value of the output of the O2 sensor may have a large error with respect to the output of the O2 sensor after the actual dead time. In the process of identifying the parameter of the model of the exhaust system, the identified value of the parameter may vary largely due to an error between the preset dead time of the model and the actual dead time thereof, i.e., a modeling error relative to a dead time element of the exhaust system, possibly resulting in an increased error of the estimated value of the output of the O2 sensor which is determined using the identified value.
According to the above techniques, since a highly stable control process such as an adaptive sliding mode control process is used as the feedback control process for generating the manipulated variable, it basically is possible to avoid a situation where the stability of the control process for converging the output of the O2 sensor to the target value would significantly be impaired.
In circumstances where the error of the estimated value of the output of the O2 sensor is relatively large, however, when the manipulated variable is generated using the estimated value and the air-fuel ratio of the air-fuel mixture is manipulated depending on the manipulated variable, the output of the O2 sensor tends to vary with respect to the target value, and the quick response of the control process converging the output of the O2 sensor to the target value is liable to be lowered.
The applicant of the present application has proposed a technique for variably setting the preset dead time of the air-fuel manipulating system depending on the rotational speed, etc. of the internal combustion engine in view of the fact that the actual dead time of the air-fuel manipulating system changes depending on the rotational speed, etc. of the internal combustion engine, as disclosed in Japanese laid-open patent publication No. 11-324767 or U.S. Pat. No. 6,188,953. The proposed technique, however, does not take into account the fact that the dead time of the exhaust system, which affects the control of the output of the O2 sensor more largely than the dead time of the air-fuel ratio manipulating system, changes depending on the operating state of the internal combustion engine, and has a predetermined fixed value as the preset dead time of the exhaust system. Therefore, the technique disclosed in the above publication also causes the above drawbacks.
The present invention has been made in view of the above background. It is an object of the present invention to provide an apparatus for and a method of controlling the air-fuel ratio of an internal combustion engine to compensate for the effect of the dead times of an exhaust system including a catalytic converter and an air-fuel ratio manipulating system including the internal combustion engine and hence to increase the purifying capability of the catalytic converter in a system for manipulating the air-fuel ratio to converge the output of an exhaust gas sensor such as an O2 sensor or the like disposed downstream of the catalytic converter to a predetermined target value to achieve an appropriate purifying capability of the catalytic converter. It is also an object of the present invention to provide a recording medium storing a program for controlling an air-fuel ratio appropriately with a computer.